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-rw-r--r--buch/chapters/40-eigenwerte/images/Makefile88
-rw-r--r--buch/chapters/40-eigenwerte/images/minmax.tex268
2 files changed, 178 insertions, 178 deletions
diff --git a/buch/chapters/40-eigenwerte/images/Makefile b/buch/chapters/40-eigenwerte/images/Makefile
index 54b36d5..4d882f0 100644
--- a/buch/chapters/40-eigenwerte/images/Makefile
+++ b/buch/chapters/40-eigenwerte/images/Makefile
@@ -1,44 +1,44 @@
-#
-# Makefile
-#
-# (c) 2020 Prof Dr Andreas Müller, Hochschule Rappersil
-#
-all: sp.pdf nilpotent.pdf kernbild.pdf kombiniert.pdf \
- wurzelapprox.pdf wurzel.pdf dimjk.pdf jknilp.pdf \
- normalform.pdf minmax.pdf
-
-sp.pdf: sp.tex sppaths.tex
- pdflatex sp.tex
-
-sppaths.tex: spbeispiel.m
- octave spbeispiel.m
-
-nilpotent.pdf: nilpotent.tex
- pdflatex nilpotent.tex
-
-kernbild.pdf: kernbild.tex bild2.jpg kern2.jpg
- pdflatex kernbild.tex
-
-kombiniert.pdf: kombiniert.tex kombiniert.jpg
- pdflatex kombiniert.tex
-
-wurzelapprox.pdf: wurzelapprox.tex wa.tex
- pdflatex wurzelapprox.tex
-
-wa.tex: wa.m
- octave wa.m
-
-wurzel.pdf: wurzel.tex
- pdflatex wurzel.tex
-
-dimjk.pdf: dimjk.tex
- pdflatex dimjk.tex
-
-jknilp.pdf: jknilp.tex
- pdflatex jknilp.tex
-
-normalform.pdf: normalform.tex
- pdflatex normalform.tex
-
-minmax.pdf: minmax.tex
- pdflatex minmax.tex
+#
+# Makefile
+#
+# (c) 2020 Prof Dr Andreas Müller, Hochschule Rappersil
+#
+all: sp.pdf nilpotent.pdf kernbild.pdf kombiniert.pdf \
+ wurzelapprox.pdf wurzel.pdf dimjk.pdf jknilp.pdf \
+ normalform.pdf minmax.pdf
+
+sp.pdf: sp.tex sppaths.tex
+ pdflatex sp.tex
+
+sppaths.tex: spbeispiel.m
+ octave spbeispiel.m
+
+nilpotent.pdf: nilpotent.tex
+ pdflatex nilpotent.tex
+
+kernbild.pdf: kernbild.tex bild2.jpg kern2.jpg
+ pdflatex kernbild.tex
+
+kombiniert.pdf: kombiniert.tex kombiniert.jpg
+ pdflatex kombiniert.tex
+
+wurzelapprox.pdf: wurzelapprox.tex wa.tex
+ pdflatex wurzelapprox.tex
+
+wa.tex: wa.m
+ octave wa.m
+
+wurzel.pdf: wurzel.tex
+ pdflatex wurzel.tex
+
+dimjk.pdf: dimjk.tex
+ pdflatex dimjk.tex
+
+jknilp.pdf: jknilp.tex
+ pdflatex jknilp.tex
+
+normalform.pdf: normalform.tex
+ pdflatex normalform.tex
+
+minmax.pdf: minmax.tex
+ pdflatex minmax.tex
diff --git a/buch/chapters/40-eigenwerte/images/minmax.tex b/buch/chapters/40-eigenwerte/images/minmax.tex
index f661d5b..cf81834 100644
--- a/buch/chapters/40-eigenwerte/images/minmax.tex
+++ b/buch/chapters/40-eigenwerte/images/minmax.tex
@@ -1,134 +1,134 @@
-%
-% minmax.tex -- minimum und maximum
-%
-% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
-%
-\documentclass[tikz]{standalone}
-\usepackage{amsmath}
-\usepackage{times}
-\usepackage{txfonts}
-\usepackage{pgfplots}
-\usepackage{csvsimple}
-\usetikzlibrary{arrows,intersections,math}
-\begin{document}
-\def\skala{1}
-\begin{tikzpicture}[>=latex,thick,scale=\skala]
-
-\definecolor{darkgreen}{rgb}{0,0.5,0}
-
-\def\mittellinie{
- plot[domain=0:6.2832,samples=400]
- ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159))})
-}
-
-\begin{scope}
- \fill[color=darkgreen!20]
- plot[domain=0:6.2832,samples=360]
- ({\x},{sin(180*\x/3.1415)})
- --
- plot[domain=6.2832:0,samples=360]
- ({\x},{cos(180*\x/3.1415)})
- -- cycle;
- \foreach \x in {0.5,1,...,6}{
- \draw[color=darkgreen]
- ({\x},{sin(180*\x/3.1415)})
- --
- ({\x},{cos(180*\x/3.1415)});
- }
-
- \node[color=darkgreen] at (2,-0.8) [left] {$|f(x)-g(x)|$};
- \draw[color=darkgreen,line width=0.3pt] (2,-0.8) -- (2.5,-0.7);
-
- \draw[color=blue,line width=1.4pt] plot[domain=0:6.29,samples=360]
- ({\x},{sin(180*\x/3.1415)});
- \draw[color=red,line width=1.4pt] plot[domain=0:6.29,samples=360]
- ({\x},{cos(180*\x/3.1415)});
- \draw[color=purple!50,line width=1.4pt] \mittellinie;
- \node[color=purple!50] at (6.2832,0.5) [right] {$\frac12(f(x)+g(x))$};
-
- \draw[->] (-0.1,0) -- (6.5,0) coordinate[label={below:$x$}];
- \draw[->] (0,-1.1) -- (0,1.3) coordinate[label={right:$y$}];
-
-
- \xdef\x{2}
- \node[color=blue] at (\x,{sin(180*\x/3.1415)}) [above right] {$f(x)$};
- \pgfmathparse{2.5*3.14159-\x}
- \xdef\x{\pgfmathresult}
- \node[color=red] at (\x,{cos(180*\x/3.1415)}) [above left] {$g(x)$};
-
-\end{scope}
-
-\draw[->,line width=4pt,color=gray!40] ({3.1415-1},-1.3) -- ({3.1415-2.3},-3);
-\draw[->,line width=4pt,color=gray!40] ({3.1415+1},-1.3) -- ({3.1415+2.3},-3);
-
-\node at ({3.1415-1.75},-2.15) [left] {$\frac12(f(x)+g(x))+\frac12|f(x)-g(x)|$};
-\node at ({3.1415+1.75},-2.15) [right] {$\frac12(f(x)+g(x))-\frac12|f(x)-g(x)|$};
-
-\def\s{(-0.1)}
-
-\begin{scope}[xshift=-3.4cm,yshift=-4.6cm]
- \fill[color=darkgreen!20]
- \mittellinie
- --
- plot[domain=6.2832:0,samples=400]
- ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)+abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})
- -- cycle;
- \foreach \x in {0.5,1,...,6}{
- \draw[color=darkgreen]
- ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)+abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})
- --
- ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159))});
- }
- \draw[color=darkgreen,line width=1.4pt]
- plot[domain=6.2832:0,samples=400]
- ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)+abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))});
-
- \node[color=darkgreen] at (2,-0.3) [left] {$|f(x)-g(x)|$};
- \draw[color=darkgreen,line width=0.3pt] (2,-0.3) -- (2.5,0.2);
-
- \draw[color=purple!50,line width=1.4pt] \mittellinie;
- \pgfmathparse{0.75*3.1415+\s}
- \xdef\x{\pgfmathresult}
- \node[color=darkgreen] at (\x,{sin(180*\x/3.1415)}) [above right]
- {$\max(f(x),g(x))$};
- \node[color=purple!50] at ({1.25*3.1415},-0.7) [below]
- {$\frac12(f(x)+g(x))$};
- \draw[->] (-0.1,0) -- (6.5,0) coordinate[label={$x$}];
- \draw[->] (0,-1.1) -- (0,1.3) coordinate[label={right:$y$}];
-\end{scope}
-
-
-\begin{scope}[xshift=+3.4cm,yshift=-4.6cm]
- \fill[color=darkgreen!20]
- \mittellinie
- --
- plot[domain=6.2832:0,samples=400]
- ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)-abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})
- -- cycle;
- \foreach \x in {0.5,1,...,6}{
- \draw[color=darkgreen]
- ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)-abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})
- --
- ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159))});
- }
- \draw[color=darkgreen,line width=1.4pt]
- plot[domain=6.2832:0,samples=400]
- ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)-abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))});
-
- \node[color=darkgreen] at (3,0.3) [right] {$|f(x)-g(x)|$};
- \draw[color=darkgreen,line width=0.3pt] (3,0.3) -- (2.5,-0.4);
-
- \draw[color=purple!50,line width=1.4pt] \mittellinie;
- \pgfmathparse{0.75*3.1415-\s}
- \xdef\x{\pgfmathresult}
- \node[color=darkgreen] at (\x,{cos(180*\x/3.1415)}) [below left]
- {$\min(f(x),g(x))$};
- \node[color=purple!50] at ({0.25*3.1415},0.7) [above right]
- {$\frac12(f(x)+g(x))$};
- \draw[->] (-0.1,0) -- (6.5,0) coordinate[label={$x$}];
- \draw[->] (0,-1.1) -- (0,1.3) coordinate[label={right:$y$}];
-\end{scope}
-
-\end{tikzpicture}
-\end{document}
-
+%
+% minmax.tex -- minimum und maximum
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\definecolor{darkgreen}{rgb}{0,0.5,0}
+
+\def\mittellinie{
+ plot[domain=0:6.2832,samples=400]
+ ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159))})
+}
+
+\begin{scope}
+ \fill[color=darkgreen!20]
+ plot[domain=0:6.2832,samples=360]
+ ({\x},{sin(180*\x/3.1415)})
+ --
+ plot[domain=6.2832:0,samples=360]
+ ({\x},{cos(180*\x/3.1415)})
+ -- cycle;
+ \foreach \x in {0.5,1,...,6}{
+ \draw[color=darkgreen]
+ ({\x},{sin(180*\x/3.1415)})
+ --
+ ({\x},{cos(180*\x/3.1415)});
+ }
+
+ \node[color=darkgreen] at (2,-0.8) [left] {$|f(x)-g(x)|$};
+ \draw[color=darkgreen,line width=0.3pt] (2,-0.8) -- (2.5,-0.7);
+
+ \draw[color=blue,line width=1.4pt] plot[domain=0:6.29,samples=360]
+ ({\x},{sin(180*\x/3.1415)});
+ \draw[color=red,line width=1.4pt] plot[domain=0:6.29,samples=360]
+ ({\x},{cos(180*\x/3.1415)});
+ \draw[color=purple!50,line width=1.4pt] \mittellinie;
+ \node[color=purple!50] at (6.2832,0.5) [right] {$\frac12(f(x)+g(x))$};
+
+ \draw[->] (-0.1,0) -- (6.5,0) coordinate[label={below:$x$}];
+ \draw[->] (0,-1.1) -- (0,1.3) coordinate[label={right:$y$}];
+
+
+ \xdef\x{2}
+ \node[color=blue] at (\x,{sin(180*\x/3.1415)}) [above right] {$f(x)$};
+ \pgfmathparse{2.5*3.14159-\x}
+ \xdef\x{\pgfmathresult}
+ \node[color=red] at (\x,{cos(180*\x/3.1415)}) [above left] {$g(x)$};
+
+\end{scope}
+
+\draw[->,line width=4pt,color=gray!40] ({3.1415-1},-1.3) -- ({3.1415-2.3},-3);
+\draw[->,line width=4pt,color=gray!40] ({3.1415+1},-1.3) -- ({3.1415+2.3},-3);
+
+\node at ({3.1415-1.75},-2.15) [left] {$\frac12(f(x)+g(x))+\frac12|f(x)-g(x)|$};
+\node at ({3.1415+1.75},-2.15) [right] {$\frac12(f(x)+g(x))-\frac12|f(x)-g(x)|$};
+
+\def\s{(-0.1)}
+
+\begin{scope}[xshift=-3.4cm,yshift=-4.6cm]
+ \fill[color=darkgreen!20]
+ \mittellinie
+ --
+ plot[domain=6.2832:0,samples=400]
+ ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)+abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})
+ -- cycle;
+ \foreach \x in {0.5,1,...,6}{
+ \draw[color=darkgreen]
+ ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)+abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})
+ --
+ ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159))});
+ }
+ \draw[color=darkgreen,line width=1.4pt]
+ plot[domain=6.2832:0,samples=400]
+ ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)+abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))});
+
+ \node[color=darkgreen] at (2,-0.3) [left] {$|f(x)-g(x)|$};
+ \draw[color=darkgreen,line width=0.3pt] (2,-0.3) -- (2.5,0.2);
+
+ \draw[color=purple!50,line width=1.4pt] \mittellinie;
+ \pgfmathparse{0.75*3.1415+\s}
+ \xdef\x{\pgfmathresult}
+ \node[color=darkgreen] at (\x,{sin(180*\x/3.1415)}) [above right]
+ {$\max(f(x),g(x))$};
+ \node[color=purple!50] at ({1.25*3.1415},-0.7) [below]
+ {$\frac12(f(x)+g(x))$};
+ \draw[->] (-0.1,0) -- (6.5,0) coordinate[label={$x$}];
+ \draw[->] (0,-1.1) -- (0,1.3) coordinate[label={right:$y$}];
+\end{scope}
+
+
+\begin{scope}[xshift=+3.4cm,yshift=-4.6cm]
+ \fill[color=darkgreen!20]
+ \mittellinie
+ --
+ plot[domain=6.2832:0,samples=400]
+ ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)-abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})
+ -- cycle;
+ \foreach \x in {0.5,1,...,6}{
+ \draw[color=darkgreen]
+ ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)-abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})
+ --
+ ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159))});
+ }
+ \draw[color=darkgreen,line width=1.4pt]
+ plot[domain=6.2832:0,samples=400]
+ ({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)-abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))});
+
+ \node[color=darkgreen] at (3,0.3) [right] {$|f(x)-g(x)|$};
+ \draw[color=darkgreen,line width=0.3pt] (3,0.3) -- (2.5,-0.4);
+
+ \draw[color=purple!50,line width=1.4pt] \mittellinie;
+ \pgfmathparse{0.75*3.1415-\s}
+ \xdef\x{\pgfmathresult}
+ \node[color=darkgreen] at (\x,{cos(180*\x/3.1415)}) [below left]
+ {$\min(f(x),g(x))$};
+ \node[color=purple!50] at ({0.25*3.1415},0.7) [above right]
+ {$\frac12(f(x)+g(x))$};
+ \draw[->] (-0.1,0) -- (6.5,0) coordinate[label={$x$}];
+ \draw[->] (0,-1.1) -- (0,1.3) coordinate[label={right:$y$}];
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+